Raffle winners ... and a question

Next, you have to multiply the losing probabilities from each of the drawings. That equals 0.9998. Finally, subtract it from one: 1 - 0.9998 = 0.0002. That is the probability of winning at least once.

So, how does that number compare to the stated chances of winning? 1/5000 = 0.0002.

Conclusion: no need to sue the club over misstated chances of winning!

On a side note: the staff of BMW CCA would like to congratulate the winners of the 2012 Car of Your Dreams Raffle, and give a huge THANK YOU to everyone who purchased a ticket for making this year a resounding success!

You might want to take a look at those numbers again. Your eyes are playing tricks on you. It isn't 1 - 0.9998, it is 1 - 0.99998. So its 0.00002 vs 0.0002.

So If someone buys 100 tickets the first day, they all go into a standalone drawing? One ticket is pulled and he/she is no longer eligible to win in the remaining drawings?

Would it be better to state there is a 9 in 45000 chance of winning?

It is a good question. I wonder which would bring in the most buyers. Personally, if buying 100 tickets, I'd much rather be buying into 100/5000 odds than 100/45,000, even if it means I only get 1 shot.

OK, I am not a statistics expert, but why would you multiply them? Every time they spin the barrel and pull a number is an independent event with independent odds.

If you do what you are saying, then each ticket on the last draw has a .02% chance of winning. With 44992 tickets in there, that's a nearly 900% total chance, yes? How is that possible?

Although, I think maybe what you are saying is that your 1/45000 chance plus your 1/44999 chance plus .... etc etc... means you get a 1/5000 chance. So it is your cumulative chances. I think I may understand that mathematically, but my logical side is telling me something is wrong there. I can't seem to get past the fact that my ticket is still 1 in over 44990 every time someone reaches their hand in there.

BTW, I was hoping someone could clear up the statistical side for me, so I'm glad for the posts and the chance to discuss.

Although, I think maybe what you are saying is that your 1/45000 chance plus your 1/44999 chance plus .... etc etc... means you get a 1/5000 chance. So it is your cumulative chances. I think I may understand that mathematically, but my logical side is telling me something is wrong there. I can't seem to get past the fact that my ticket is still 1 in over 44990 every time someone reaches their hand in there.

Bingo! I think the thing that is most confusing about probability is that it is a calculation over the course of all of the drawings combined (that's why you have to multiply them). You can't apply the total chances to one specific drawing. So, the 1/5000 chances applies to a member winning one of the nine drawings, not one specific drawing of the nine.

As long as I can remember, about 3 decades back, all the entries have been placed in one barrel. Way back, only one car was awarded each year but there were far fewer members to buy tickets. The stated odds used to be far better than 1 in 5,000, but that's another discussion. The "cause," by the way, is the BMW CCA treasury.
Think about this. Since we can buy more than 1 ticket and all tickets are in one barrel, it is possible for one person to win more than one car. It would be highly unlikely, but I see nothing in the rules to prevent that.

Think about this. Since we can buy more than 1 ticket and all tickets are in one barrel, it is possible for one person to win more than one car. It would be highly unlikely, but I see nothing in the rules to prevent that.

True. It is possible to win more than one car. Theoretically, one person buying nine tickets could have won them all. If we do this long enough somebody will.